For which of the following solutions must we consider the ionization of water when calculating the pH or pOH?
(a) 3 × 10−8 M HNO3
(b) 0.10 g HCl in 1.0 L of solution
(c) 0.00080 g NaOH in 0.50 L of solution (d) 1 × 10−7 M Ca(OH)2
(e) 0.0245 M KNO3
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To determine which of the given solutions we must consider the ionization of water when calculating the pH or pOH, we need to understand when water ionization becomes significant.
Water undergoes a process called autoionization, where a small fraction of water molecules dissociate into ions. This can be represented by the following equilibrium reaction:
H2O ⇌ H+ + OH-
The concentration of the ions H+ (hydrogen ions) and OH- (hydroxide ions) in pure water at 25°C is 1.0 × 10^-7 M each. This equilibrium constant is known as the ion product of water (Kw) and is equal to 1.0 × 10^-14 at 25°C.
If the concentration of H+ ions or OH- ions from another solute is significant in relation to the concentration of H+ and OH- ions due to water autoionization, then we need to consider the ionization of water in calculating the pH or pOH.
Let's analyze each given solution to determine if the ionization of water needs to be considered:
(a) 3 × 10^-8 M HNO3: This is a strong acid that fully dissociates in water. Since the concentration of H+ ions from HNO3 is much higher than the concentration of H+ ions from water autoionization, we don't need to consider water ionization.
Therefore, the answer is NO.
(b) 0.10 g HCl in 1.0 L of solution: We need to convert the grams of HCl to moles and then divide by the volume to find the concentration in mol/L. HCl is also a strong acid and fully dissociates in water. Again, the concentration of H+ ions from HCl is much higher than the concentration of H+ ions from water autoionization, so we don't need to consider water ionization.
Therefore, the answer is NO.
(c) 0.00080 g NaOH in 0.50 L of solution: Similar to the previous case, we need to convert the grams of NaOH to moles and then divide by the volume to find the concentration in mol/L. NaOH is a strong base and also fully dissociates in water. Since the concentration of OH- ions from NaOH is much higher than the concentration of OH- ions from water autoionization, we don't need to consider water ionization.
Therefore, the answer is NO.
(d) 1 × 10^-7 M Ca(OH)2: In this case, we have a weak base, Ca(OH)2. It will partially dissociate in water to form Ca2+ and OH- ions. Since the concentration of OH- ions from Ca(OH)2 is comparable to the concentration of OH- ions from water autoionization, we must consider water ionization when calculating the pH or pOH.
Therefore, the answer is YES.
(e) 0.0245 M KNO3: KNO3 is a salt that fully dissolves in water to form K+ and NO3- ions. However, since none of these ions are H+ or OH-, they don't have any impact on water ionization. We can safely ignore the ionization of water.
Therefore, the answer is NO.
In summary, we must consider the ionization of water (water autoionization) when calculating the pH or pOH for solution (d) 1 × 10^-7 M Ca(OH)2.